Flux of a Ratchet Model and Applications to Processive Motor Proteins

In this paper, we investigate the stationary probability current (or flux) of a Brownian ratchet model as a function of the flipping rate of the fluctuating potential barrier. It is shown that, with suitably selecting the parameters' values of the ratchet system, we can get the negative resonant activation, the positive resonant activation, the double resonant activation, and the current reversal, for the stationary probability current versus the flipping rate. The appearance of these phenomena is the result of the cooperative effects of the potential's dichotomous fluctuations and the internal thermal fluctuations on the evolution of the flux versus the flipping rate of the fluctuating potential barrier. In addition, some applications of our results to the motor proteins are discussed.     

Escape over fluctuating potential barrier for system only driven by dichotomous noise

The escape for the mean first passage time (MFPT) over the fluctuating potential barrier for system only driven by a dichotomous noise is investigated. It is found that, in some circumstances, the dichotomous noise can induce the resonant activation for the MFPT over the fluctuating potential barrier, but in other circumstances, it cannot. There are two resonant activations for the MFPT. One is the MFPT as a function of the flipping rate of the fluctuating potential barrier, the other is the MFPT as a function of the transition rate of the dichotomous noise.     

Escape over Fluctuating Barrier for a Stochastic Model of Motor Proteins in the Case of Environmental Perturbation

We study the mean first passage time (MFPT) over the fluctuatingpotential barrier for a stochastic model of motor proteins in the case of environmental perturbation proposed by J.H. LI et al. [Phys. Rev. E57 (1998) 39171. The MFPT is derived for a particle over the fluctuating potential barrier. It is shown that (i) there is resonant activation for the MFPT as a function of the flipping rate of the fluctuating potential barrier; (ii) the additive and multiplicative noises can weaken the resonant activation, but the correlations between them enhance the resonant activation; (iii) the susceptibility of the resonant activation to the multiplicative noise is far larger than that to the additive noise.     

Multi-Resonant-Activation for a System Only Driven by Multi-State Noise

We consider the escape of the particles multi-state noise. It is shown that, the noise can make over fluctuating potential barrier for a system only driven by a the particles escape over the fluctuating potential barrier in some circumstances; but in other circumstances, it can not. If the noise can make the particle escape over the fluctuating potential barrier, the mean first passage time （MFPT） can display the phenomenon of multi-resonant-activation. For this phenomenon, there are two kinds of resonant activation to appear. One is resonant activation for the MFPTs as the function of the flipping rates of the fluctuating potential barrier; the other is that for the MFPTs as the functions of the transition rates of the multi-state noise.     

Mean First Passage Time for System with Fluctuating Potential Barrier and Coupled Noise

In this paper we study the mean first passage time (MFPT) over a fluctuation potential barrier driven by a coupled noise. It is shown that the MFPT over the fluctuation potential barrier displays resonant activations as the function of the flipping rate of the fluctuation potential barrier, and as the function of the dichotomous noise transition rate.     

Escape from a fluctuating system: a master equation and trapping approach

We present a general solution for the mean exit time in a system with on-site fluctuations between two configurations described by a master equation. The coupled configurations represent a spatially discretized version of an escape over a fluctuating barrier [C. R. Doering and J. C. Gadoua, Phys. Rev. Lett. 69, 2318 (1992)], and passage through modulating channels. Based on the general properties of the mean exit time, we obtain a simple solution for a coupled "birth" and "death" case that exhibits resonant activation. Within this exactly solvable model we derive analytically the optimal fluctuating rate, which is sensitive to the initial condition and scales as 1/n, where n is the system size. Our approach unifies a number of escape problems and points towards the generality of resonant activation.     

Resonances while surmounting a fluctuating barrier

Electronic analog experiments on escape over a fluctuating potential barrier are performed for the case when the fluctuations are caused by Ornstein-Uhlenbeck noise (OUN). In its dependence on the relation between the two OUN parameters (the correlation time tau and noise strength Q) the nonmonotonic variation of the mean escape time T as a function of tau can exhibit either a minimum (resonant activation), or a maximum (inhibition of activation), or both these effects. The possible resonant nature of these features is discussed. We claim that T is not a good quantity to describe the resonancelike character of the problem. Independently of the specific relation between the OUN parameters, the resonance manifests itself as a maximal lowering of the potential barrier during the escape event, and it appears for tau of the order of the relaxation time toward the metastable state.     

Transport and dynamical properties of inertial ratchets

In this paper we discuss the dynamics and transport properties of a massive particle in a ratchet type potential immersed in a dissipative environment. The directional currents and characteristics of the motion are studied as the specific frictional coefficient varies, finding that the stationary regime is strongly dependent on this parameter. The maximal Lyapunov exponent and the current show large fluctuations and inversions, therefore for some range of the control parameter, this inertial ratchet could originate a mass separation device. Also an exploration of the effect of a random force on the system is performed.     

Brownian motion in fluctuating periodic potentials

This work deals with the overdamped motion of a particle in a fluctuating one-dimensional periodic potential. If the potential has no inversion symmetry and its fluctuations are asymmetric and correlated in time, a net flow can be generated at finite temperatures. We present results for the stationary current for the case of a piecewise linear potential, especially for potentials being close to the case with inversion symmetry. The aim is to study the stationary current as a function of the potential. Depending on the form of the potential, the current changes sign once or even twice as a function of the correlation time of the potential fluctuations. To explain these current reversals, several mechanisms are proposed. Finally, we discuss to what extent the model is useful to understand the motion of biomolecular motors.     

Stochastic resonance, reverse-resonance, and resonant activation induced by a multi-state noise

In this paper, we investigate the periodic response for a linear system driven by a multiplicative multi-state noise (which is composed of the multiplication of two dichotomous noises) to an input temporal oscillatory signal, and the escape of Brownian particles over the fluctuating potential barrier for a system with a piece-wise linear potential and driven by an additive multi-state noise (which is also composed of the multiplication of two dichotomous noises). For the first system, we get the stochastic resonance phenomenon for the amplitude of the periodic response vs. the two dichotomous noise strengths, and the phenomenon of reverse-resonance for the amplitude of the periodic response vs. k, which represents the asymmetry degree of the dichotomous noises. For the second system, we obtain the resonant activation phenomenon, for which the mean first passage time of the Brownian particles over the fluctuating potential barrier shows a minimum as the function of the transition rates of the multi-state noise.     

Transport in a fluctuating potential

We study the overdamped motion of a particle in a fluctuating one-dimensional periodic potential. The potential has no inversion symmetry, and the fluctuations are correlated in time. At finite temperatures, a stationary current is induced. The amplitude and the direction of the current depend on the details of the noise process that is responsible for the potential fluctuations. We discuss several limiting situations for a general case. Furthermore we calculate the current in the case of a piecewise linear potential for different noise processes and parameters. A detailed discussion of the results is given, including a discussion of the mechanism that is responsible for the current reversal. We compare the present results with results for transport in a ratchet-like potential due to a fluctuating force. We also discuss the biological relevance of the present models for molecular motors. We present a model for the motion of molecular motors that explains why similar molecular motors can move in different directions.     

Persistent current and transmission probability in the Aharonov-Bohm ring with an embedded quantum dot

Persistent current and transmission probability in the Aharonov-Bohm (AB) ring with an embedded quantum dot (QD) are studied using the technique of the scattering matrix. For the first time, we find that the persistent current can arise in the absence of magnetic flux in the ring with an embedded QD. The persistent current and the transmission probability are sensitive to the lead-ring coupling and the short-range potential barrier. It is shown that increasing the lead-ring coupling or the short-range potential barrier causes the suppression of the persistent current and the increasing resonance width of the transmission probability. The effect of the potential barrier on the number of the transmission peaks is also investigated. The dependence of the persistent current and the transmission probability on the magnetic flux exhibits a periodic property with period of the flux quantum.     

Effective classical stochastic theory for quantum tunneling

The ensemble mean equations for a classical particle moving stochastically obtain the form of fluid equations. When applying the Madelung transformation to write the Schrödinger equation in a fluid-like form we find that the equations are equivalent to the classical ensemble mean equations if an additional force is added to the equations. The latter can be expressed as a pressure gradient force of a fluctuating pressure with zero mean. Here we analyze the mechanism of quantum tunneling through a rectangular potential barrier from this perspective. We find that despite of the vanishing of the mean of the pressure fluctuations their local non zero gradients enable the tunneling by balancing the counter external potential gradients at the two sides of the potential barrier. Consequently, for stationary solutions, the ensemble mean kinetic energy remains unchanged across the boundaries of the barrier.     

延迟基因开关体系的稳定性及转变动力学

对延迟基因开关体系的稳定性及转变动力学进行了系统的研究．通过前向流采样及延迟随机模拟方法,获得了相空间稳态分布、转变路径和速率以及转变态系综的分布等信息．数值结果表明,基因开关体系中的延迟会减小稳态之间的间距,增大体系在转变态的布居．此外,转变速率也会随着延迟时间的增大单调增加,这些现象都说明延迟会削弱双稳基因开关体系的稳定性．转变路径由两种转录因子蛋白质的总的粒子数的差和操纵子位点的状态来描述,对转变路径的数值分析表明转录和翻译过程导致的延迟会显著影响转变动力学．特别是对于转变态系综而言,操纵子结合两种不同二聚体概率的差异随着延迟时间的增加逐渐加大.     

Theory of slightly fluctuating ratchets

We consider a Brownian particle moving in a slightly fluctuating potential. Using the perturbation theory on small potential fluctuations, we derive a general analytical expression for the average particle velocity valid for both flashing and rocking ratchets with arbitrary, stochastic or deterministic, time dependence of potential energy fluctuations. The result is determined by the Green’s function for diffusion in the time-independent part of the potential and by the features of correlations in the fluctuating part of the potential. The generality of the result allows describing complex ratchet systems with competing characteristic times; these systems are exemplified by the model of a Brownian photomotor with relaxation processes of finite duration.     

Active Brownian motion models and applications to ratchets

We give an overview over recent studies on the model of Active Brownian Motion (ABM) coupled to reservoirs providing free energy which may be converted into kinetic energy of motion. First, we present an introduction to a general concept of active Brownian particles which are capable to take up energy from the source and transform part of it in order to perform various activities. In the second part of our presentation we consider applications of ABM to ratchet systems with different forms of differentiable potentials. Both analytical and numerical evaluations are discussed for three cases of sinusoidal, staircaselike and Mateos ratchet potentials, also with the additional loads modelled by tilted potential structure. In addition, stochastic character of the kinetics is investigated by considering perturbation by Gaussian white noise which is shown to be responsible for driving the directionality of the asymptotic flux in the ratchet. This stochastically driven directionality effect is visualized as a strong nonmonotonic dependence of the statistics of the right versus left trajectories of motion leading to a net current of particles. Possible applications of the ratchet systems to molecular motors are also briefly discussed.     

Constructive influence of noise-flatness in correlation ratchets

The influence of noise-flatness on overdamped motion of Brownian particles in a 1D periodic system with a simple sawtooth potential subjected to both unbiased thermal noise and three-level telegraph noise is considered. The exact formula for the stationary probability flux (current) is presented. The phenomenon of multiple current reversals and some topological properties of the hypersurface of zero current in the parameter space of noises are investigated and illustrated by phase diagrams. The conditions for the existence of four current reversals versus the switching rate of nonequilibrium noise are given. An alternative interpretation of the results in terms of cross-correlation between two dichotomous noises is presented.     

一维晶格中费曼棘齿-棘爪热机

研究了一维晶格中费曼棘齿-棘爪热机模型. 用粒子的概率主方程来描述粒子在晶格中的动力学特性, 推导出热流、 功率和效率的表达式. 通过数值计算分析势垒高度、 外力和温比对热流以及热机功率和效率的影响. 研究表明: 在粒子稳态概率流为零时, 存在非零的热流从高温库流入低温库, 类似于经典不可逆卡诺模型中的热漏; 热漏的存在使得热机的效率远远小于卡诺效率, 功率与效率之间为闭合的关系曲线, 热机为不可逆热机; 对热机性能参数进行优化, 可以使热机工作在最优性能状态下.     

Transport properties and current inversion by white Gaussian noise in a coupled ratchet model

We have found, by varying two parameters, several stationary trajectories in a system consisting in many elastically coupled particles that are placed in a periodic ratchet potential on a ring. The system is assumed to be over-damped and driven by an external potential that is periodic both in space and time. The transport properties of these orbits are quite different and their values are quantified. The symmetries allow us to study the orbits with and without the presence of thermal fluctuations and there is found current inversions due to the addition of white Gaussian noise.